Recent content by EV33

Thank you so much. My function is continuous.

Homework Statement I was trying to prove something and I ended up in a situation similar to, (limit t\rightarrow0)(limit s\rightarrow0) f(x+s,y+t) =(limit s\rightarrow0)(limit t\rightarrow0)f(x+s,y+t) My question is when does this equality hold. I can't find it anywhere...

Homework Statement I am curious if all modules contain 0. Homework Equations A left R-module M over the ring R consists of an abelian group (M, +) and an operation R × M → M such that certain properties hold... The Attempt at a Solution The definition of a module says that it is an...

Homework Statement I am curious, if I,J, and M are ideals of the commutative ring R, and M/I\subseteqJ/I, then M\subseteqJHomework Equations M/I = { m+I : m is in M} J/I = { j+I : j is in J} I\subseteqR is an ideal if 1.) if a and b are in I then a+b is in I 2.) if r is in R and a is in I...

Ok. So I get 32=9=0 mod 9. So 32 is an element of 9z. By definition 3 is an element of 9z. So I get that it holds for this case. That's what I was supposed to get right?

By what you wrote makes me think you were thinking of the converse of my statement. Were you just showing that it, in fact, is an iff statement?

Homework Statement In the process of trying to prove something else I found it would be helpful if rn\inI, where I is an ideal, n\inN, and r\inR and R is a ring, then r is in I. Homework Equations I is an ideal if a\inI and b\inI then a+b\inI, a\inI and r\inR then ar\inI, and I is not the empty...

Sorry, this should have have been posted in the calculus and beyond section.

Homework Statement My question is just on the definition of L∞. Is L∞=Lp where p=∞, i.e., is a measurable function in L∞ if ∫Alf(x)l∞<∞? Homework Equations *L∞: The space of all bounded measurable functions on [0,1] (bounded except for possibly on a set of measure zero) *A measurable...

Homework Statement My question is would I be allowed to say, if lf+-\phil<ε/(2\mu(E) then ∫E lf+-\phil<ε/2 Homework Equations E is the set in which we are integrating over. \mu is the measure \varphi is a simple function f+ is the non-negative part of the function f. The Attempt...

Homework Statement I was wondering if we Let E be some set such that f-1(E) is measurable then so is f-1(E)c.Homework Equations If the set A is measurable then so is its compliment. The Attempt at a Solution I think the statement is true because f-1(E) is just a set and thus its compliment...

I have a simple question about differentials. I have been taught two ways to find the differential and my questions is in what situations do I use each one? simply speaking these are the 2 ways 1.) just take the partials of each component function and throw them in a matrix 2.) Let f be the...

Never Mind. I figured it out.

Homework Statement Does anyone know the process for finding the differential of of f:S→S' where S,S' are surfaces. My textbook explains how to do this when f is a vector valued function but in the problem that I am working on I have something like f(x,y)=(g(x),h(x),j(y)) rather than something...

Homework Statement I have this theorem which I am having trouble understanding due to notation. Theorem: Define S,S'\subseteqℝ3 to be surfaces. Let f:S→S' be a smooth map. f is a local isometry if for all p in S, and all w1,w2 in TpS, <w1,w2>=<dfp(w1),dfp(w2)>. The thing I don't...